Abstract Rockfalls are common in the steep and vertical slopes of the Campania carbonate massifs and ridges, and frequently represent the main threat to the anthropogenic environment, potentially damaging urban areas, scattered houses, roads, etc. Despite the generally limited volumes involved, the high velocity of movement (from few to tens of metres per second) poses rockfalls among the most dangerous natural hazards to man. Evaluating the rockfall hazard is not an easy task, due to the high number of involved factors, and particularly to the difﬁculty in determining the properties of the rock mass. In this paper, we illustrate the assessment of the rockfall hazard along a small area of the Sorrento Peninsula (Campania region, southern Italy). Choice of the site was determined by the presence of a road heavily frequented by vehicles. In the area, we have carried out detailed ﬁeld surveys and software simulations that allow generating simple rockfall hazard maps. Over twenty measurement stations for geo-mechanical characterization of the rock mass have been distributed along a 400-m-long slope of Mount Vico Alvano. Following the internationally established standards for the acquisition of rock mass parameters, the main kinematics have been recognized, and the discontinuity families leading to the different failures identiﬁed. After carrying out ﬁeld experiments by artiﬁcially releasing a number of unstable blocks on the rock cliff, the rockfall trajectories along the slope were modelled using 2-D and 3-D programs for rockfall analysis. The results were exploited to evaluate the rockfall hazard along the threatened element at risk.

In this work. mining activities. we present the results of an attempt to evaluate rockfall hazard in a section of the Sorrento Peninsula.
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. More speciﬁcally. In Italy. Geological and morphological information required to perform the rockfall simulations was obtained from existing topographical and geological maps. Cinque et al. to the north. Morphology is characterized by steep to very steep slopes. temperature changes. analysing rockfall trajectories observed in the ﬁeld when unstable rock blocks were released artiﬁcially. and the hazard posed by rockfalls is severe (Parise 2002). Speciﬁcally. controlled chieﬂy by block faulting. Flageollet and Weber 1996). to the south. 2005). melting of snow or permafrost. Cruden and Varnes 1996) make rockfalls dangerous to the population. 1). and the infrastructure (Whalley 1984. is as a ‘‘hot spot’’ with frequent fatal rockfall events. from the Gulf of Salerno. the Sorrento Peninsula. pipe leakage. The structural setting is dominated by NW–SE. the result of the complex interaction between uplift. and during dedicated ﬁeld surveys. crop out. along the Tyrrhenian coast between Naples and Salerno. which locally exhibit a strike-slip component (Patacca and Scandone 1987. stress relief following deglaciation. rockfalls represent a primary cause of landslide fatalities (Guzzetti 2000. a sequence of dolomite and limestone is overlaid by Miocene sandstone. freeze–thaw cycles of water. Human-induced causes of rockfalls include undercutting of rock slopes. and by pyroclastic deposits resulting from the explosive activity of the Vesuvius and the Campi Flegrei volcanoes. blasting. the built-up environment. Rockfall hazard in the area is determined through numerical simulations of rockfall trajectories. The results obtained with the different rockfall modelling software are compared and tested against independent information on rockfall occurrence obtained during the ﬁeld surveys. It is characterized by a NW-dipping monocline where sedimentary and volcanic rocks. and erosion. or trafﬁc.188
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Keywords
Rockfall Á Hazard Á Modelling Á Sorrento Peninsula Á Italy
1 Introduction Rockfalls are a type of fast mass movement common in mountain areas worldwide. 2010) reveals that in the Campania region the geological and morphological conditions are prone to rockfalls. preserved chieﬂy in small structural depressions. including earthquakes. The simulations are performed using four computer codes. intense rainfall. the study is aimed at determining rockfall hazard in an 850-m-long segment of a road built along the steep slopes of Monte Vico Alvano (Fig. and vibrations caused by excavations. Individual or multiple rock blocks with volumes ranging from a few cubic decimetres to thousands of cubic metres and travelling at rapid to extremely rapid velocity ([3 m min-1. In particular. by Quaternary alluvial and marine sediments. inefﬁcient drainage.and NE– SW-trending normal faults and thrusts. Mesozoic to Recent in age. 2003. 1993). and root penetration and wedging.
2 Regional and local setting The Sorrento Peninsula is a SW–NE-trending horst that separates the Campania plain. volcanic activity. Evans and Hungr 1993. Inspection of the geographical distribution of fatal landslide events in Italy (Salvati et al. Rockfalls are triggered by a variety of natural and human-induced causes (Guzzetti and Reichenbach 2010). Guzzetti et al.

Miocene in age. protection of the transportation network from rockfalls is problematic in the Sorrento Peninsula (Budetta and Santo 1994). Cretaceous in age. roads in the area are frequently affected by rockfalls. and by thin and partially reworked pyroclastic deposits. Calcaterra and Santo 2004). The top of the ridge is an old (relict). 3 Conglomerates (Upper Pleistocene). covered by sandstone and calcareous marl. consisting of layered limestone. Due to the local morphology. where they have resulted in multiple catastrophic events that have caused damage to the population. The study area is located along the southern slopes of Monte Vico Alvano (Fig. 2 Slope debris (Holocene–Pleistocene). 8 boundary of the investigated slope. 1). the size of the individual failures depends on the mechanical properties of the rock. In the rockfall source area. the main transportation network runs primarily along the seashore and at the bottom of high and steep to sub-vertical rock slopes prone to rockfall failures. low gradient surface.Nat Hazards (2012) 61:187–201
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Fig. 9 Via Lavinola
Mass movements are abundant in the Sorrento Peninsula. 1 Location of the study area and geological map: 1 Fall pyroclastic deposits (Holocene–Upper Pleistocene). separated from the foothills by steep to sub-vertical fault-scarp-slopes affected by multiple slope instabilities. chieﬂy rockfalls. the infrastructure. 6 Tectonic discontinuities (dashed when inferred). which in places is highly fractured.
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. 7 Strata bedding. 4 Sandstones and calcareous marls (Lower Tortonian). including a pumice layer from the 79 AD eruption of Vesuvius described by Pliny the Younger. For this reason. and the built-up environment (Budetta and Santo 1994. Given the extent of the rockfall problem. 5 Limestones (Upper Cretaceous).

Many fractures were found open. Nevertheless. layered and fractured limestone). 2. where terrain is inaccessible or difﬁcult to reach (Terzaghi 1965.e. At each of the twenty measuring stations. The individual discontinuities were analysed visually to determine prevailing direction of movements based on local kinematic indicators. with aperture chieﬂy lower than 5 mm and rarely larger than 10 mm. care was taken in the identiﬁcation and quantiﬁcation of weathering effects on the individual discontinuities. Along the talus slopes below the rock cliff. Fig. number. blocks of
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. However. Dershowitz and Einstein 1988).and meso-scopic structural analyses were performed to obtain quantitative information on the type. Figs. In addition to measuring the geo-mechanical properties of the individual discontinuities. Hudson and Priest 1983) (Table 1. To obtain geo-mechanical information for a spatially distributed and sufﬁciently large number of sites on the rock cliff. with only a few blocks with volume VL [ 2 m3 (Table 1). Data on the attitude of the individual discontinuities collected in the ﬁeld were plotted on equal-area (Lambert) and on equal-angle (Wulff). First. The equal-area plots were used for density analysis and for the identiﬁcation of the attitude of the main sets of discontinuities. Parise 2008). Most of the open fractures were empty and did not contain ﬁlling material. at each measuring station the shape and size of individual or multiple unstable rock blocks were estimated. the location and the reduced number of accessible sites were such that the information obtained at these sites was not sufﬁcient for a reliable characterization of the geomechanical properties of the rock mass. alpine techniques were used. macro. This is an indication that most of the slope failures were old.. The volume of the single blocks was obtained by measuring the distance between adjacent discontinuities and by estimating the pervasiveness and depth of the discontinuities in the rock mass. At each measuring station. Given the type of rock cropping out in the area (i. including slickensides on fault and joint planes. in addition to bedding. The analysis revealed that. Given the spacing of the discontinuities (Table 1). 3). and ﬁlling of the rock discontinuities (Hoek and Bray 1981. orientation. a detailed geological and structural survey conducted in the period from 2002 to 2007 allowed determining the geo-mechanical characteristics of the rockfall source areas and obtaining information on rockfall trajectories. Some of the large boulders were covered by soil and vegetation. the geological and structural survey was difﬁcult to perform. Investigators climbed on the rock cliff and performed a systematic survey of the rock face along horizontal and vertical proﬁles. LaPointe and Hudson 1985. at least three sets of discontinuities—including bedding—were identiﬁed. persistence. This is a common problem in mountain areas. The information obtained at individual measuring stations positioned along the proﬁles was integrated with comparable information obtained at known rockfall source areas (Guadagno 2005). resulting from a combination of physical alteration and chemical solution (Fookes and Hawkins 1988. six sets of discontinuities are present in the study area (Table 1. in recent years several rockfalls have occurred. aperture. The volume of the boulders was VL \ 1 m3. a number of boulders were identiﬁed and measured.190
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3 Geo-mechanical analysis In the study area. possibly as a result of fragmentation at rockfall impact points. lower hemisphere stereographic projections (steronets). 3). Due to the morphology of the area. which forced the local authorities to close the road. The most frequent rock blocks were small in size. ranging in volume 10 \ VL \ 50 cm3. spacing. Geo-mechanical data were collected adopting the standards proposed by the International Society of Rock Mechanics (ISRM 1978). the most accessible sites were studied. characterized by very steep and locally inaccessible slopes.

and the geometrical relationship with the different sets of discontinuities. 4). The equal-angle data were used to perform a set of Markland and Matheson tests (Markland 1972. 2 Histograms showing the main parameters of surveyed discontinuity systems
generally small to medium size (10 \ VL \ 50 cm3) are separated from the rock mass. Results of both the tests indicate that most of the potential block failures are of the fall or of the topple types. the most prone sets for detachment of rock blocks are K2 and K3 (Table 1). Given the slope aspects in the study area (N 145 and N 235). 5). The Matheson test allows identiﬁcation of the likely movements in a rock slope by zoning in the stereoplot those sectors more prone to produce different types of instability mechanisms (an example of the test output is presented as Fig.
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.192
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Fig. posing a threat both to the road at the base of the slope and to the trafﬁc along the road. Potentially unstable conditions are most abundant in the upper part of the rock cliff. Falls are locally associated with the presence of overhanging. Topples are associated chieﬂy with the presence of release joint systems (Fig. unsupported slabs. Matheson 1983). Some of the blocks are balanced precariously (Brune 1996). the result of selective erosion of the clay beds separating limestone beddings. theoretically. where limestone layers are thinner and the effect of the stress release is largest. The Markland test compares the orientation of the local slope with the orientation of the discontinuities and the internal angle of friction (the frictional component of the shear strength) of the rock to determine which discontinuity makes the rock mass unstable.

Jones et al. This is justiﬁed because the output of the spatially distributed SMR classiﬁcation was used to identify the areas more likely to generate rockfalls and as input for the numerical modelling of rockfalls (Dorren 2003. a 2D model that incorporates the Colorado Rockfall Simulation Program (CRSP) (GeoStru 2004. The SMR index is obtained from the Rock Mass Rating (RMR) system (Bieniawski 1976. F2. For the interpolation. geographically coherent with a digital elevation model (DEM) available for the study area. 3 Stereoplot showing the six families of tectonic discontinuities (K1 to K6) and the strata bedding (S1 and S2)
The geo-mechanical data obtained at the 20 measurement stations were superimposed on a 5 m 9 5 m grid. (3) GeoRock 3D. 6). Pfeiffer et al. a total energy
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. 1991. F4 = 15 (Singh and Goel 1999). (2) Rotomap. The SMR classiﬁcation index was determined at each measuring station. 2-dimensional (2D) and 3-dimensional (3D) numerical models for rockfall simulation were used.
4 Rockfall modelling To ascertain rockfall hazard in the study area. For natural slopes. F3) and one factor related to the slope excavation method (F4). 2006). The gridded information was used to obtain a spatially distributed evaluation of the stability of the rock cliff. 2000). in ﬁve classes (Table 2). Pfeiffer and Bowen 1989. modulated by the addition of four adjustment factors.Nat Hazards (2012) 61:187–201
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Fig. the lowest (worst) class determined at each measuring station was selected. and interpolated over the entire rock cliff (Fig. Dorren et al. 1989). including three factors to consider the effects of joint and slope orientation (F1. including the following: (1) GeoRock. 1991). which implements a 3D lumped mass model (Scioldo 2006). adopting the Slope Mass Rating (SMR) geo-mechanical classiﬁcation index (Romana 1985.

K3 in blue. Red colour marks the poles and great circles intersections potentially unstable
conservation model (GeoStru 2009). and starting velocity of the falling block. the GeoRock 2D software was used to obtain preliminary estimates of the maximum distance to the ground of the rockfall trajectories and of the energy dissipated at impact points. and (3) values for the roughness coefﬁcient. 4 Example of the Matheson test performed on one of the measuring station (rock face oriented 330/85). to model the loss of energy at the impact points. a 3D kinematic (lumped mass) distributed modelling software. First. 2004). and (4) Stone (Guzzetti et al. Discontinuity families: K1 in purple. the GeoRock 2D software requires the following factors (Table 3): (1) information on the shape. To perform a simulation.194
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Fig. (2) the distance to the ground of the rockfall trajectory. K2 in red. Outputs of the modelling software include the following: (1) the type of movement of a block along a falling trajectory. (2) values for the normal and the tangential energy restitution coefﬁcients. d wedge failure. size (volume). For this preliminary 2D simulation. bedding S in green. Numerical modelling of rockfall trajectories in the study area was performed in steps. weight. b ﬂexural toppling. eight representative
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. Yellow colour indicates the stereoplot areas prone to possible movements of the following type: a toppling failure. used to model the loss of energy where the block is rolling. and (3) the energy of the block along the falling trajectory. c planar sliding.

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Fig. Twenty-four unstable blocks identiﬁed on the rock cliff were measured to obtain accurate information on their shape and size. This empirical information obtained in the ﬁeld was used to perform a new set of parametric rockfall simulations. and then artiﬁcially released. Analysis of this ﬁrst set of simulations revealed that the modelling results were not in agreement with ﬁeld data. we performed a set of ﬁeld experiments. using the GeoRock 2D software. including the location of individual rockfall boulders along the slope. To overcome this problem. For each released block. c toppling failure Table 2 Romana classiﬁcation. b complex movement deriving from interaction among the blocks. releasing from each point 50 boulders that were ‘‘launched’’ using a wide range of energy restitution and rolling friction coefﬁcients from the literature. 5 Some failure mechanisms identiﬁed during the surveys: a shear failure controlled by tensional release and bedding planes. Pfeiffer and Bowen 1989). The ensemble of the
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. used for a ﬁrst zonation of the slope and for the identiﬁcation of the rockfall source areas Class SMR Stability Failure type V 0–20 Highly unstable Large planar failures and rotational slumps IV 21–40 Unstable Planar failures along several joints and/or large wedges III 41–60 Partially stable Planar failures along some joints and/or many wedges II 61–80 Stable Some failures of isolated blocks I 81–100 Completely stable
rockfall source areas were identiﬁed along the cliff top. using normal and tangential restitution coefﬁcients obtained from the literature (Hoek 1987. likely evolving to fall. with planar slide and/or toppling. A different set of simulation was performed for each of the 24 blocks. and an ensemble of fourteen topographic proﬁles was traced from the source areas down the slope along the steepest local terrain gradient. and to obtain better estimates for the energy restitution and rolling friction coefﬁcients. Bieniawski 1989. The mismatch was attributed chieﬂy to incorrect values for the normal and the tangential restitution coefﬁcients adopted for the simulations. the main impact points and the location of the end point of the rockfall trajectory (the point of deposition) were determined. A ﬁrst set of 2D rockfall simulation was obtained along the fourteen topographic proﬁles (Fig. 7).

Interpolation was performed using kriging. the maximum energy and the height of the blocks. For the 3D modelling of the rockfall trajectories. moved within the slight valley in the central part of the slope and were able to reach the road. The digital terrain representation consisted of a digital elevation model (DEM) with a 5 m 9 5 m ground resolution. the trajectories computed by Rotomap (Fig. 6 Zonation of the study area according to the SMR index. in fact. the limit angle. Explanation: green colour is Class II (SMR = 61–80). a detailed representation of the topographic surface obtained using a terrestrial laser scanner was used. and the simulated rockfall trajectories that matched the ﬁeld data were identiﬁed. the rockfall source areas. and the energy restitution and rolling friction coefﬁcients.196
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Fig. 8a) conﬁrm those observed during the removal operations of some limestone blocks. At Mount Vico Alvano. The energy restitution and rolling friction coefﬁcients used for these modelled rockfall trajectories were taken as representative of the ﬁeld conditions (see the numbers in Table 3) and used for further 3D modelling of the rockfalls. The outputs are the geometry of the block trajectories. posing a serious threat for a long part of the communication route. and blue colour is Class IV (SMR = 21–40)
obtained rockfall trajectories were compared to the empirical data.
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. This regularly spaced digital terrain representation was obtained by interpolating irregularly spaced elevation points. Rotomap (Scioldo 2006) is a lumped mass model that requires a digital elevation model (DEM). the arrival points. the initial velocity of the block. yellow colour is Class III (SMR = 41–60). the maximum angle deviation. Most of the detached blocks.

6 m3 1. two defensive barriers were planned and put in place (location shown in Fig. and a kinematical simulation is performed.53 0. a physically based software capable of modelling rockfall processes in three dimensions and of providing information relevant to ascertain rockfall hazard. The outputs are the trajectory (Fig. 8b). The residual hazard along the road was eventually assessed taking into account the presence of these rockfall defence measures (the rockfall retaining structures).6 m3 1.32 2D Total energy conservation No Spherical 4.9 0. The trajectories derived from the 3D simulations (Rotomap and GeoRock 3D) were used to establish the location of the retaining structures. and (3) the coefﬁcients of dynamic rolling friction and of normal and tangential energy restitution. with Rotomap and GeoRock 3D.53 0. Figure 8 shows the cumulative count of rockfall trajectories that passed through each cell and allows evaluating the residual rockfall hazard along the road posed by the areas identiﬁed along the cliff top as more representative rockfall source areas. the source area (including the number of blocks to be launched).Nat Hazards (2012) 61:187–201 Table 3 Main inputs required by the computer programs GeoRock 2D Trajectory analysis Physical model DEM Shape of the block Size of the block Weight of the block Initial velocity of the block Normal restitution coefﬁcient Limestone Debris and volcaniclastic cover Tangential restitution coefﬁcient Limestone Debris and volcaniclastic cover Source area Number of blocks launched from a source area 0.e. Following the simulations performed with GeoRock (2D). height and kinetic energy of the blocks in movement. 2002.2 9 10 kg 1 m s-1
4
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Rotomap 3D Lumped mass Yes – 4.9 0.2 9 104 kg 1 m s-1
Stone 3D Lumped mass Yes – – – 1 m s-1
Multiple (cell) 20
Using similar input data.53 0. The GeoRock 3D (GeoStru 2009) requires as input a digital elevation model. The falling boulder is considered dimensionless (i.2 9 10 kg 1 m s-1
4
GeoRock 3D 3D Lumped mass Yes – 4.. a point).32 0.8 Multiple 25 0. the initial velocity of the block. we prepared rockfall models with GeoRock 3D and Stone. For the purpose. the density and diameter of the block.9 0.8 Multiple Variable. The input data we used for the simulation include (1) the location of the eight rockfall detachment areas. (2) a digital elevation model. 9).32 0. whilst height and energy values of the barriers were determined using the output obtained by the 2D analysis. velocity.53 0.8 Individual 50 0. The software adopts a ‘‘lumped-mass’’ approach to model rockfalls. the normal and tangential energy restitution coefﬁcients. 2004). to protect the sections of the road that were most likely to be hit by the moving rockfalls. we used Stone (Guzzetti et al.9 0.
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.32 0. depending on the size of the source area 0.8 0.6 m3 1.

and related traces downslope following the highest gradients and the topographic constraints
Fig. and b GeoRock 3D
5 Conclusions We determined rockfall hazard along the slopes of Monte Vico Alvano through a combination of geological and structural surveys. 8 Trajectories computed for eight source areas using a Rotomap. in particular
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. 7 Main source areas identiﬁed along the slope. and 2.and 3-dimensional rockfall numerical modelling (Table 2).198
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Fig. The study pointed out to the role played by ﬁeld surveys.

Field observation allowed us to compute different restitution coefﬁcients that were exploited to perform rockfall back-analysis. Assuming that the retaining structures are effective. It appeared therefore of crucial importance the direct observation of falling blocks during the experimental ﬁeld tests. the model prepared with Stone reveals that the residual rockfall hazard along the road can be acceptable from the areas classiﬁed as more unstable but should be better evaluated considering all the unstable portion of the cliff. we obtained not realistic simulations. the 2D models were used to calculate the energy values useful to design the defence structures. In conclusion. The second point to highlight regards the reliability of the restitution coefﬁcients available in the literature. 9 Cumulative count of rockfall trajectories using Stone. whilst the 3D models were used to choose the location for the protective measures.
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. Field surveys restricted to the more accessible sites can in fact negatively affect the results of structural surveys. since the collected data represent only partially the real pattern and distribution of the discontinuities in the rock mass. Using coefﬁcients acquired from the literature. The so determined output energy values were eventually used to design the retaining structures. fundamental for the correct characterization of the rock mass and the identiﬁcation of the rockfall source areas.Nat Hazards (2012) 61:187–201
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Fig. based upon the simulated trajectories followed by the blocks. The correct position of the retaining structures and the residual hazard along the road was also evaluated with Stone. The simulation consider the presence of rockfall retaining structures (green lines)
those carried out by means of alpine techniques along the vertical cliffs.